Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Survey

Transcript

PRE-ALGEBRA Lesson 6-1 Warm-Up PRE-ALGEBRA Ratios and Unit Rates (6-1) What is a “ratio”? ratio: a comparison of two numbers by division – There are three ways to compare two numbers: a a to b a:b b read as “to” How do you write a ratio? You can write a ratio to compare a part to a part or part to a whole. The first item being compared is always the first number and the second item being compared is the second number of the ratio. Example: A recipe calls for 4 cups of cereal and 2 cups of pretzels. Write this as a ratio. PRE-ALGEBRA Ratios and Unit Rates (6-1) What is a “rate”? rate: a ratio that compares two quantities measured in different units. Example: 120 miles is read as “120 miles ‘per’ or ‘each’ 4 hours” 4 hours What is a “unit rate”? unit rate: the rate in which the denominator is 1 (rate ‘per’ 1 unit of a given quantity) - Unit rate is used in everyday life to determine the best value. It can be found by simplifying the fraction to a denominator of “1” or simply dividing the numerator (top number) by the denominator (bottom number. Example: 120 miles 4 = 30 miles or 120 4 = 30 mph 1 hours 4 hours 4 The above unit rate is read as “30 miles ‘per’ hour” (30 m/h or 30 mph) PRE-ALGEBRA Ratios and Unit Rates LESSON 6-1 Additional Examples Find the unit rate for typing 145 words in 5 minutes. number of words number of minutes = 145 words 5 minutes = 29 words/minute Write a rate comparing words to minutes. Divide. The unit rate is 29 words per minute. PRE-ALGEBRA Ratios and Unit Rates LESSON 6-1 Additional Examples Convert 30 gal/min to cups/second. 30 gal 30 gal/min = 1 min 130 gal = 1 min 16 c • 1 gal 816 c • 1 gal 8c = s 1 min • 60 s • 1 min 260 s Convert gallons to cups and minutes to seconds. Divide the common factors and units. 1 Simplify. 30 gal/min equals 8 c/s. PRE-ALGEBRA Ratios and Unit Rates LESSON 6-1 Additional Examples The table shows prices for different packages of index cards. Which size has the lowest unit cost? Size (cards) Price 100 $2.70 50 $1.30 25 $.75 100 cards: price number of cards $2.70 100 cards = $.027/card 50 cards: price number of cards $1.30 50 cards Find the = $.026/card unit costs. 25 cards: price number of cards $.75 25 cards = $.03/card The 50-card pack has the lowest unit cost. PRE-ALGEBRA Ratios and Unit Rates LESSON 6-1 Additional Examples Painting several rooms will take 36 person-hours. How long will it take for 4 painters? It takes 36 persons to complete painting several rooms in 1 hour. To find the number of hours it will take 4 persons to complete the job, divide. 36 person-hours = 9 hours 4 persons Divide the number of person-hours by the number of workers. It will take 9 hours for 4 painters to paint the rooms. Check Since person • hours = hours, the units check. persons PRE-ALGEBRA Ratios and Unit Rates LESSON 6-1 Lesson Quiz Find each unit rate. 1. You pay $4.50 for 2 gallons of orange juice. $2.25/gal 2. You pay $21.60 for a 20-lb bag of dog food. $1.08/lb 3. A bird flies at a speed of 384 in./s. What is its 1,920 ft/min speed in units of ft/min? 4. A job takes 96 person-days. How many workers are needed to complete the job in 24 days? 4 PRE-ALGEBRA